On the number line, what is the distance between the point 2x and the

BY theory of distances and absolute values, distance between 2 points a and b on the number line = |a-b|.

Thus distance between 2x and 3x = |2x-3x| = |x|. Thus the questions asks |x| = ?

Per statement 1, |-x-x| =16 ---> |x|=8 . Sufficient.

Per statement 2, |x-3x| = 16 ---> |x|=8. Sufficient.

Both statements are sufficient on their own. Hence, D is the correct answer.
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

On the number line, what is the distance between the point 2x and the point 3x ?

1. On the number line, distance between the point -x and the point x is 16 .
2. On the number line, distance between the point x and the point 3x is 16


When you modify the original condition and the question, since the distance is an absolute value, |3x-2x|=|x|=? is a question. There is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), |x-(-x)|=16, |2x|=16, |x|=8, which is unique and sufficient.
For 2), |3x-x)|=16, |2x|=16, |x|=8, which is unique and sufficient. Therefore the answer is D.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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